Ms. Jackson Wants To Rent A Medium Truck For A Week. It Will Cost The Weekly Fee Plus $\$0.20$ Per Mile Driven. Let $m =$ The Number Of Miles Ms. Jackson Drives During The Week. Use This Information And The Table Below To
Ms. Jackson's Truck Rental Dilemma: A Mathematical Exploration
Ms. Jackson is planning to rent a medium truck for a week, and she needs to determine the total cost of the rental. The cost will be the weekly fee plus an additional charge of $0.20 per mile driven. In this article, we will use mathematical concepts to explore the relationship between the number of miles driven and the total cost of the rental.
Let's break down the information provided:
- The weekly fee for renting the truck is not specified.
- The additional charge per mile driven is $0.20.
- We need to find the total cost of the rental, which is the sum of the weekly fee and the additional charge for the miles driven.
Let's define the variables:
- m: the number of miles Ms. Jackson drives during the week.
- C: the total cost of the rental, which is the sum of the weekly fee and the additional charge for the miles driven.
The cost function can be represented as:
C = weekly fee + 0.20m
We can simplify this function by letting the weekly fee be represented by a variable, say w. Then, the cost function becomes:
C = w + 0.20m
To visualize the relationship between the number of miles driven and the total cost of the rental, we can graph the cost function. Let's assume the weekly fee is $100. Then, the cost function becomes:
C = 100 + 0.20m
We can graph this function by plotting the points (0, 100), (10, 120), (20, 140), and so on.
From the graph, we can see that the cost of the rental increases linearly with the number of miles driven. This means that for every additional mile driven, the cost of the rental increases by $0.20.
Suppose Ms. Jackson wants to know how many miles she can drive during the week without exceeding a total cost of $200. We can set up an equation using the cost function:
200 = w + 0.20m
Since we don't know the value of the weekly fee, we can't solve for the number of miles driven. However, we can express the number of miles driven in terms of the weekly fee:
m = (200 - w) / 0.20
In this article, we explored the relationship between the number of miles driven and the total cost of renting a medium truck. We defined the variables, represented the cost function, graphed the function, and interpreted the graph. We also solved for the number of miles driven in terms of the weekly fee. By using mathematical concepts, we can better understand the problem and make informed decisions.
| Weekly Fee | Cost per Mile | Total Cost |
|---|---|---|
| $100 | $0.20 | $100 + 0.20m |
| $150 | $0.20 | $150 + 0.20m |
| $200 | $0.20 | $200 + 0.20m |
- [1] "Truck Rental Fees." [Website], [Date of Access].
- [2] "Cost Functions." [Textbook], [Publisher], [Year].
Ms. Jackson's Truck Rental Dilemma: A Q&A Guide
In our previous article, we explored the relationship between the number of miles driven and the total cost of renting a medium truck. We defined the variables, represented the cost function, graphed the function, and interpreted the graph. We also solved for the number of miles driven in terms of the weekly fee. In this article, we will answer some frequently asked questions about Ms. Jackson's truck rental dilemma.
A: The weekly fee for renting a medium truck is not specified in the problem. However, we can assume a value for the weekly fee to make calculations easier. Let's assume the weekly fee is $100.
A: According to the problem, you will be charged $0.20 per mile driven.
A: The total cost of the rental is the sum of the weekly fee and the additional charge for the miles driven. We can represent this as:
C = w + 0.20m
where C is the total cost, w is the weekly fee, and m is the number of miles driven.
A: To calculate the number of miles you can drive without exceeding a total cost of $200, you can set up an equation using the cost function:
200 = w + 0.20m
Since we don't know the value of the weekly fee, we can't solve for the number of miles driven. However, we can express the number of miles driven in terms of the weekly fee:
m = (200 - w) / 0.20
A: If you drive more miles than you planned, you will be charged an additional $0.20 per mile driven. To calculate the additional cost, you can multiply the number of extra miles driven by the cost per mile:
Additional Cost = 0.20 * (m - planned miles)
A: Yes, you can rent a truck for a shorter or longer period of time. However, the cost per mile driven will remain the same. To calculate the total cost, you can multiply the number of miles driven by the cost per mile, and then add the weekly fee.
A: If you want to rent a truck with a different weekly fee, you can simply substitute the new weekly fee into the cost function:
C = new weekly fee + 0.20m
In this article, we answered some frequently asked questions about Ms. Jackson's truck rental dilemma. We provided formulas and examples to help you calculate the total cost of the rental, the number of miles you can drive without exceeding a total cost, and the additional cost if you drive more miles than planned. By understanding the cost function and the variables involved, you can make informed decisions when renting a truck.
| Weekly Fee | Cost per Mile | Total Cost |
|---|---|---|
| $100 | $0.20 | $100 + 0.20m |
| $150 | $0.20 | $150 + 0.20m |
| $200 | $0.20 | $200 + 0.20m |
- [1] "Truck Rental Fees." [Website], [Date of Access].
- [2] "Cost Functions." [Textbook], [Publisher], [Year].